{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fa079261",
   "metadata": {},
   "source": [
    "# **<font size=4 color=#BB3D00 face=微软雅黑>波形生成：时间向量和正弦波</font>**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "692dad96",
   "metadata": {},
   "source": [
    "## <font size=3  face=微软雅黑>**※Matlab案例**</font> "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd4b6313",
   "metadata": {},
   "source": [
    "网址：https://ww2.mathworks.cn/help/signal/gs/waveform-generation-time-vectors-and-sinusoids-1.html    \n",
    "描述：本案例由1个示例构成。    \n",
    "### - <font color=DarkOrChid size=3>示例1：生成时间向量和正弦波</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a52776b",
   "metadata": {},
   "source": [
    "## <font size=3 face=微软雅黑>**※Python案例**</font> "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fed90440",
   "metadata": {},
   "source": [
    "针对以上案例，采用Python语言实现。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d18c128e",
   "metadata": {},
   "source": [
    "### - <font color=DarkOrChid size=3>示例1：生成时间向量和正弦波</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e128267",
   "metadata": {},
   "source": [
    "大多数工具箱函数要求从表示时基的向量开始。例如，假设以 1000 Hz 采样频率生成数据。合适的时间向量是**np.linspace(0,1,1001)**。    \n",
    "在给定 t 的情况下，可以创建由两个正弦波组成的示例信号 y，第一个正弦波的频率为 50 Hz，另一个的频率为 120 Hz 且幅值是第一个正弦波的两倍。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8ebaec45",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "707c1c28",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.linspace(0,1,1001)\n",
    "#Generate a time vector in steps of 1 ms\n",
    "y = np.sin(2 * np.pi * 50 * t )+np.sin(2 * np.pi * 120 * t )\n",
    "#create a sample signal y consisting of two sinusoids, one at 50 Hz and one at 120 Hz"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e43f2962",
   "metadata": {},
   "source": [
    "由向量 t 构成的新变量 y 的长度也是 1001 个元素。您可以将正态分布的白噪声添加到信号中，并绘制前 50 个点："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "abf34de4",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 1001\n",
    "white_noise = np.random.standard_normal(size=n)\n",
    "#Generate Gaussian white noise\n",
    "yn = y + white_noise\n",
    "plt.plot(t[1:50],y[1:50])\n",
    "#add normally distributed white noise to the signal and plot the first 50 points\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
